{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:4CQUKDR2GPTE6OWJAWZ44OQ2LI","short_pith_number":"pith:4CQUKDR2","canonical_record":{"source":{"id":"2512.16193","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.AO","submitted_at":"2025-12-18T05:33:16Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.DS","math.MP","nlin.PS"],"title_canon_sha256":"0f8f3596356988ee686aa883b3f4c7f638db1494826a801b0c42d78890ee8d45","abstract_canon_sha256":"90291308d4bbc67de2935edbefae2d25c5f62e2632bd936db43706dddfabeafb"},"schema_version":"1.0"},"canonical_sha256":"e0a1450e3a33e64f3ac905b3ce3a1a5a140c8daa29af0081cbf50d949bf7c657","source":{"kind":"arxiv","id":"2512.16193","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.16193","created_at":"2026-06-24T01:14:24Z"},{"alias_kind":"arxiv_version","alias_value":"2512.16193v2","created_at":"2026-06-24T01:14:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.16193","created_at":"2026-06-24T01:14:24Z"},{"alias_kind":"pith_short_12","alias_value":"4CQUKDR2GPTE","created_at":"2026-06-24T01:14:24Z"},{"alias_kind":"pith_short_16","alias_value":"4CQUKDR2GPTE6OWJ","created_at":"2026-06-24T01:14:24Z"},{"alias_kind":"pith_short_8","alias_value":"4CQUKDR2","created_at":"2026-06-24T01:14:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:4CQUKDR2GPTE6OWJAWZ44OQ2LI","target":"record","payload":{"canonical_record":{"source":{"id":"2512.16193","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.AO","submitted_at":"2025-12-18T05:33:16Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.DS","math.MP","nlin.PS"],"title_canon_sha256":"0f8f3596356988ee686aa883b3f4c7f638db1494826a801b0c42d78890ee8d45","abstract_canon_sha256":"90291308d4bbc67de2935edbefae2d25c5f62e2632bd936db43706dddfabeafb"},"schema_version":"1.0"},"canonical_sha256":"e0a1450e3a33e64f3ac905b3ce3a1a5a140c8daa29af0081cbf50d949bf7c657","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:14:24.076481Z","signature_b64":"U7Opg66kWIqsHNIidbxIu2TWLseJEXeTo7zSJ1GXMcGMiuZXYAf001n8h8eWpNilT9pH9GcadVX2Zdik+OjZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0a1450e3a33e64f3ac905b3ce3a1a5a140c8daa29af0081cbf50d949bf7c657","last_reissued_at":"2026-06-24T01:14:24.075994Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:14:24.075994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.16193","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-24T01:14:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZqaACKmsDep63bDJvGaTrz6jjL3xMp2MX4BejlU2nlHEismh+yoBQfGIZAHZO1NYfcJGqUTKx3u04vfYORWrDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:29:37.292079Z"},"content_sha256":"737d8db0626190bf52ded2fdbdbefd31c0909b3d19dc7d8d6e06cc5aaeffd642","schema_version":"1.0","event_id":"sha256:737d8db0626190bf52ded2fdbdbefd31c0909b3d19dc7d8d6e06cc5aaeffd642"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:4CQUKDR2GPTE6OWJAWZ44OQ2LI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Emergence of higher-order interactions in systems of coupled Kuramoto oscillators with time delay","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.DS","math.MP","nlin.PS"],"primary_cat":"nlin.AO","authors_text":"Bob Rink, Hiroya Nakao, Keisuke Taga, Narumi Fujii, Riccardo Muolo","submitted_at":"2025-12-18T05:33:16Z","abstract_excerpt":"We show that higher-order interactions naturally emerge from time-delayed pairwise coupling in Kuramoto oscillators. By expanding the delayed pairwise coupling to the second order, we derive a delay-free Kuramoto model possessing both pairwise and three-body interactions. Numerical simulations and stability analysis demonstrate that the three-body Kuramoto model and the time-delayed pairwise Kuramoto model exhibit qualitatively consistent synchronization transitions under appropriate conditions. In particular, the bistability arising in the time-delayed Kuramoto model is accounted for by the t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.16193","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.16193/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-24T01:14:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dXEjpJm9zPl4gftGHF2B1txd/UZTf09/KRtmADeQBUgXjzrDdGaIQXC/nwR51iJyEKBLwavgQm8ZUazFPxe2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:29:37.292471Z"},"content_sha256":"a40d27acadea62ba0da72583e15ba5b01e6aa8042f2f5f947346bc8d81d41b72","schema_version":"1.0","event_id":"sha256:a40d27acadea62ba0da72583e15ba5b01e6aa8042f2f5f947346bc8d81d41b72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4CQUKDR2GPTE6OWJAWZ44OQ2LI/bundle.json","state_url":"https://pith.science/pith/4CQUKDR2GPTE6OWJAWZ44OQ2LI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4CQUKDR2GPTE6OWJAWZ44OQ2LI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-03T17:29:37Z","links":{"resolver":"https://pith.science/pith/4CQUKDR2GPTE6OWJAWZ44OQ2LI","bundle":"https://pith.science/pith/4CQUKDR2GPTE6OWJAWZ44OQ2LI/bundle.json","state":"https://pith.science/pith/4CQUKDR2GPTE6OWJAWZ44OQ2LI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4CQUKDR2GPTE6OWJAWZ44OQ2LI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4CQUKDR2GPTE6OWJAWZ44OQ2LI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"90291308d4bbc67de2935edbefae2d25c5f62e2632bd936db43706dddfabeafb","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.DS","math.MP","nlin.PS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.AO","submitted_at":"2025-12-18T05:33:16Z","title_canon_sha256":"0f8f3596356988ee686aa883b3f4c7f638db1494826a801b0c42d78890ee8d45"},"schema_version":"1.0","source":{"id":"2512.16193","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.16193","created_at":"2026-06-24T01:14:24Z"},{"alias_kind":"arxiv_version","alias_value":"2512.16193v2","created_at":"2026-06-24T01:14:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.16193","created_at":"2026-06-24T01:14:24Z"},{"alias_kind":"pith_short_12","alias_value":"4CQUKDR2GPTE","created_at":"2026-06-24T01:14:24Z"},{"alias_kind":"pith_short_16","alias_value":"4CQUKDR2GPTE6OWJ","created_at":"2026-06-24T01:14:24Z"},{"alias_kind":"pith_short_8","alias_value":"4CQUKDR2","created_at":"2026-06-24T01:14:24Z"}],"graph_snapshots":[{"event_id":"sha256:a40d27acadea62ba0da72583e15ba5b01e6aa8042f2f5f947346bc8d81d41b72","target":"graph","created_at":"2026-06-24T01:14:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2512.16193/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that higher-order interactions naturally emerge from time-delayed pairwise coupling in Kuramoto oscillators. By expanding the delayed pairwise coupling to the second order, we derive a delay-free Kuramoto model possessing both pairwise and three-body interactions. Numerical simulations and stability analysis demonstrate that the three-body Kuramoto model and the time-delayed pairwise Kuramoto model exhibit qualitatively consistent synchronization transitions under appropriate conditions. In particular, the bistability arising in the time-delayed Kuramoto model is accounted for by the t","authors_text":"Bob Rink, Hiroya Nakao, Keisuke Taga, Narumi Fujii, Riccardo Muolo","cross_cats":["cond-mat.stat-mech","math-ph","math.DS","math.MP","nlin.PS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.AO","submitted_at":"2025-12-18T05:33:16Z","title":"Emergence of higher-order interactions in systems of coupled Kuramoto oscillators with time delay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.16193","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:737d8db0626190bf52ded2fdbdbefd31c0909b3d19dc7d8d6e06cc5aaeffd642","target":"record","created_at":"2026-06-24T01:14:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"90291308d4bbc67de2935edbefae2d25c5f62e2632bd936db43706dddfabeafb","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.DS","math.MP","nlin.PS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.AO","submitted_at":"2025-12-18T05:33:16Z","title_canon_sha256":"0f8f3596356988ee686aa883b3f4c7f638db1494826a801b0c42d78890ee8d45"},"schema_version":"1.0","source":{"id":"2512.16193","kind":"arxiv","version":2}},"canonical_sha256":"e0a1450e3a33e64f3ac905b3ce3a1a5a140c8daa29af0081cbf50d949bf7c657","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0a1450e3a33e64f3ac905b3ce3a1a5a140c8daa29af0081cbf50d949bf7c657","first_computed_at":"2026-06-24T01:14:24.075994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:14:24.075994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U7Opg66kWIqsHNIidbxIu2TWLseJEXeTo7zSJ1GXMcGMiuZXYAf001n8h8eWpNilT9pH9GcadVX2Zdik+OjZDQ==","signature_status":"signed_v1","signed_at":"2026-06-24T01:14:24.076481Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.16193","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:737d8db0626190bf52ded2fdbdbefd31c0909b3d19dc7d8d6e06cc5aaeffd642","sha256:a40d27acadea62ba0da72583e15ba5b01e6aa8042f2f5f947346bc8d81d41b72"],"state_sha256":"a1b1a70d2512acc694ad3e2d08dba4e0a5f07449fcf5170756022a22394f2f6f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LP/l5DLA4LF3NLzT4Sv2IMqBf62siGdotCLCYGei567zCdrAGeeDytLJsaMmO4sM+N7fZp6LDozxfeUTVyanBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T17:29:37.327419Z","bundle_sha256":"76260652ca1d55954305c0a354dc0693f10311085a6fa0ab5717c3457b5d6d19"}}